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RAISE NOTICE is the right method.
The reason RAISE NOTICE output does not appear in clog.log is that your standard error redirection is wrong at the shell level.
You want:
psql --log-file=plog.log -f file.sql >clog.log 2>&1
That way it redirects the standard output into clog.log and then the standard error to that standard output.
The way ...

In our system we use dblink's and write to the same DB. This is an alternative approach for Oracle Autonomous Transaction.
Here I use the concept of DB link to achieve the asynchronous commit for logging. This is as same as the concept of Autonomous Transaction in Oracle.
Commits done inside the db link will not cause a commit in the main transaction.
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I spent a while in a test environment trying to reproduce your issue and have had some success. If I set up Log Shipping in its most basic form, and in such a way as to mimic your situation, everything appears to be working. However, I have found one way to configure the environment that results in messages similar to yours...
Message 1:
Message 2:
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